Note that a common issue with PIC simulations is the possible occurrence of spurious numerical heating of the macroparticles population during the simulation.
This effect, due to the so-called “finite grid instability” [1]}, [2]}, [3]}, appears when the Debye length is not resolved enough by the numerical grid. In such a case, the electrons would be numerically heated, which would hide the wave-particle interaction we are looking for. We have carefully checked that our PIC simulations are free from such numerical spurious heating, by comparing the evolution of the supra-thermal electron density in the unstable layer to the one outside the layer on both sides, where the plasma is stable, to check that the numerical heating of the electrons is negligible compared to the one arising from wave-particle interaction in the layer.
